The generator matrix

 1  0  1
 0  1  2
 0  0  1

generates a code of length 3 over Z16 who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+42x^1+591x^2+2828x^3+591x^4+42x^5+1x^6

The gray image is a code over GF(2) with n=24, k=12 and d=4.
This code was found by Heurico 1.16 in 8.96e-008 seconds.